An Integrability Condition for Simple Lie Groups II

It is shown that a simple Lie group $G$ ($\neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra of $G$. The integrability condition is the vanishing of a torsion tensor of type $(1,2)$. This is a slight improvement of an earlier result proved in [Min-Oo M., Ruh E.A., in Differential Geometry and Complex Analysis, Springer, Berlin, 1985, 205-211]

Interacting two-state Markov chains on undirected networks

It is shown that irreducible two-state continuous-time Markov chains interacting on a network in a bilinear fashion have a unique stable steady state. The proof is elementary and uses the relative entropy function.Comment: 9 pages; minor typos correcte

Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold

In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is topologically T^2 X R. In the limit, these special Lagrangians asymptotically approach a special Lagrangian cone on a torus in the conifold. Using moment map techniques we also recover the family of SO(n)-invariant special Lagrangian n-folds in the cotangent bundle of the n-sphere obtained by H. Anciaux.Comment: 22 pages, 2 figure

The development of distance education programmes for future marine engineering in the Union of Myanmar

The shipping industry is changing day after day in the areas of safety, operation, construction, manning, and management system. Seafarers need to go onboard ships with their ability and conduct being trained onboard and at the Maritime Education and Training (MET) Institute. Many of the young generation in the Union of Myanmar join seagoing ships as deck cadets or engineroom apprentices after attending mandatory maritime training courses at the Institute of Marine Technology (IMT). This dissertation deals with the MET system and the competency certification of seafarers in the Union of Myanmar in chapter 1 and chapter 2. Myanmar seafarers need proper training for them to progress in their professional knowledge while they are working onboard amongst multinational crew. Amongst other types of teaching the distance learning programme is an alternative which is a convenient and efficient education system for people who are working away from conventional institute. The distance learning institutes for seafarers conducted in Australia and Japan are observed in chapter 5. Accordingly, the IMT is the most preferable institute in the country to establish the distance learning programmes for the Myanmar mariners who are not capable to study the traditional education programmes. The methods of distance education conducted by the IMT are proposed there include how teaching should be conducted between teachers and students and what kinds of learning materials are essential to achieve the students’ progression. The effective learning programmes are discussed for mariners of ocean-going. Pre-sea training engineering apprentices at shipyards, and inland marine engineers and engine drivers

The design of semi-submersibles for minimum vertical motion

Summary available: p. [1

Bundle Constructions of Calibrated Submanifolds in R^7 and R^8

We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R^{2n}.Comment: 22 pages; for Revised Version: Minor changes, improved notation, streamlined expositio